#1) a normal distribution has a mean of 101 and a standard deviation of 4.2. what is the z-score of 105?

Answers

Answer 1

Step-by-step explanation:

z = (specific score - mean) / standard deviation

in our case

z = (105 - 101)/4.2 = 4/4.2 = 0.952380952... ≈ 0.95

as z-tables usually round the z-scores to hundredths.

Answer 2

The z-score of the normal distribution is 0.95.

What is normal distribution?

A probability distribution which is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution.

It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution shows as a "bell curve" on a graph.

Z-score: A Z-score is just a metric that quantifies how closely a value relates to a mean of a set of values. Standard deviations from of the mean are used to measure Z-score.

A Z-score of zero means the data point is actually score is the same as the mean score.

The formula for z-score is-

[tex]Z=\frac{x-\mu}{\sigma}[/tex]

Z = standard score

x  is observed value = 105

[tex]\mu[/tex] is mean of the sample 101.

[tex]\sigma[/tex] is standard deviation of the sample 4.2.

Substitute all the values in the z-score formula;

z = ( 105 - 101)/4.2

z = 0.9523..

z  = 0.95

Therefore, the z-score the given normal distribution is  0.95.

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Related Questions

A surveyor at point S locates a tree 200 meters away, at point T. The surveyor turns 120 degrees counterclockwise and locates a rock formation 150 meters away, at point R. Find the distance between the tree and the rock formation.

This will require using the law of cosines.

Answers

Answer:

190

Step-by-step explanation:

The distance between the tree and the rock formation is approximately 304.14 meters.

To find the distance between the tree (point T) and the rock formation (point R), we can use the law of cosines. The law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles.

Let's denote the unknown distance between the tree and the rock formation as 'd.'

We have a triangle with sides of lengths 200 meters (side ST), 150 meters (side SR), and d meters (side TR). The angle opposite side ST is 120 degrees.

According to the law of cosines:

d² = 200² + 150² - 2 * 200 * 150 * cos(120°)

Now, we can calculate this expression to find the value of d:

d² = 40000 + 22500 - 60000 * cos(120°)

Using the value of cos(120°) ≈ -0.5, we have:

d² = 40000 + 22500 - 60000 * (-0.5)

d² = 40000 + 22500 + 30000

d² = 92500

Taking the square root of both sides to solve for d:

d = √92500

d ≈ 304.14

Therefore, the distance between the tree and the rock formation is approximately 304.14 meters.

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Which linear inequality best represents the graph?

Answers

Answer:

[tex]3x - 4y \geqslant - 12[/tex]

Step-by-step explanation:

[tex]3x - 4y \geqslant - 12[/tex]

[tex] - 4y \geqslant - 3x - 12[/tex]

Y <= 3/4X +3

‼️help please.‼️What is the slope-intercept equation of the line with a slope
4
of and a y-intercept of 3?
5

Answers

Answer:

C

Step-by-step explanation:

according to the standard equation;

Y=mX+C

or, Y=4/5X +3

Someone plz help me I will give brainliest:)

Answers

"If we leave now," she said. "We'll be right on time."

"Do you have dear Mr. Henshaw? Alice, ask the clerk."

Blvd.

add ness to strange making it strangeness

I think that the broken tv is the subject

Answer:

1) "If we leave now" she said, "We'll be right on time.

2) "Do you have deer, Mr. Henshaw?" Alice asked the clerk.

3) blvd.

4) Er (Strang-er)

5) Television

Step-by-step explanation:

Hope this Helps!!

:D

Explain how I would use Distributive Property (GCF) to factor the following expression: 4m + 16

Answers

Answer:

4(m+4)

Step-by-step explanation:

4m+16

Rewriting

4*m + 4*4

Factor out 4

4(m+4)

can some one write a system for all of these? it would really help me rn :(

Answers

Answer: 36 and 56

Step-by-step explanation: the sum of two numbers translates into x + y = 92

If the difference would be 0 then the numbers would be equal.

Just choose which number you want to be bigger. If x is bigger then x - y = 20. If y is bigger then y - x = 20.

Let’s make x bigger so x-y=20. You can go two ways with this.

Either x=20+y because when passing one term from one side to the other you can change the sign.

Or y=x-20 because you pass “-y” to the right and it’s becomes “y” and you pass 20 to the left and it becomes -20.

Let’s go with y=x-20.

Now we replace this in the other relation:

X + Y = 92

X + (x-20) = 92

X + X - 20 = 92

2x - 20 = 92 ==> 2x = 92 + 20 ==> 2x = 112 ==> 112/2 ==> x=56

Y = x - 20 ==> y = 56 - 20 ==> y = 36.

If you choose x=20+y and replace x in the other relation you’ll find out y first and only after that you’ll find x.

Hope this helps☺️

Solve: 1/3(9x + 12) = 15

Answers

Answer:

Do u still need help

Step-by-step explanation:

Answer:

x = 11/3  

Step-by-step explanation:

1/3 (9x + 12) = 15

3x + 4 = 15

3x = 11

x = 11/3

What is the value of x?
Enter your answer in the box.
x =
Two intersection lines. Angle formed at the top is labeled 3 x plus 50 degrees. Angle formed at the bottom is labeled 6 x minus 10 degrees.

Answers

The answer is 20 degrees

Answer:

the anwser is (60-50)

Step-by-step explanation:

took the test

What is the difference in finding the exact vs approximate volume?

Answers

Answer:

An exact number is one that has no uncertainty. An example is the number of tires on a car (exactly 4) or the number of days in a week (exactly 7). An approximate number is one that does have uncertainty. ... The number can be the result of a measurement.

Step-by-step explanation:

Write the equation of the line that passes through (4, -6) and (8, 10)

Answers

Answer:

Line equation: y=4x−22

Slope: 4

Intercept: -22

Step-by-step explanation:

Sandy has 10 roses, 2 daisies, and 8 tulips. She wants to arrange all the flowers in bouquets. Each bouquet has the same number of flowers and the same type of flower. What is the greatest number of flowers that could be in a bouquet?

Answers

Answer: The greatest number of flowers that could be in a bouquet = 2

Step-by-step explanation:

Given: Sandy has 10 roses, 2 daisies, and 8 tulips.

Each bouquet has the same number of flowers and the same type of flower.

The greatest number of flowers that could be in a bouquet = GCD (10,2,8)

Since 10=2 x 5, 8 = 2 x 2 x 2

GCD (10,2,8) =2

Then, The greatest number of flowers that could be in a bouquet = 2

someone please help ​

Answers

Answer:

x = 4√3, or approximately 6.93

Step-by-step explanation:

This is a right triangle with hypotenuse 13 and side lengths x and 11.  According to the Pythagorean Theorem, x^2 + 11^2 = 13^2 = 169, or

x^2 + 121 = 169, or

x^2 = 48.

x must be a positive quantity.  Thus, x = +√48 = + √3·√16 = +4√3

Thus, x = 4√3, or approximately 6.93

Write a function rule to describe this statement-

A model is %60 of the size of the real item.

Answers

Answer:

let the size of the real item be x

then the size of model as prodived will be =

60% of X

60/100 × X

=3X/5 .

Your family is on the way to Disneyland! On the freeway you have driven for 120 minutes at a constant speed of 65 miles per hour before you stop for lunch. After lunch you get back on the freeway with a bit of traffic and drive at a constant speed of 40 miles per hour for 30 minutes before stopping for gas. How far did you drive in all? Use a ratio method.

Answers

Answer:

150 miles

Step-by-step explanation:

The scalene triangle ABC is translated 2 units to the right on a coordinate plane to form the scalene triangle DEF. The measure of segment AB=6 units, the measure of segment BC=5 units, the measure of segment CA=4 units, and m∠ABC=41°. Which of the following is a corresponding measure of triangle DEF?

Answers

Answer:

C: EF = 4 Units

Step-by-step explanation:

Which angle in the graph is vertical to ABI?

Answers

the angle that is vertical to ABI is EBH

Your store cost on a dozen eggs is $0.75, and your retail price is $2.99. You are having a promotion that discounts the
eggs 10%. What is your margin on the discounted eggs?

Answers

Answer:

$1.94

Step-by-step explanation:

The Margin on the discounted eggs is $2.392.

What is Unitary Method?

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Store cost on a dozen eggs is $0.75,

and retail price is $2.99.

The amount of discount is 10%

Discount given on $2.99

= 10% of 2.99

= 0.1 x 2.99

= 0.299

Cost of eggs after discount =2.99-0.299= 2.691

So, The discounted eggs costs $2.691.

Hence, The difference in store cost and discounted cost = 2.691- 0.299                      

                                                                                               = $2.392

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verify the segments are parallel

Answers

Step-by-step explanation:

I don't have a answer but try photo math app it might help you a lil

Max buys six donuts and a 300ml carton of juice for $3.50,susie buys four donuts and two 300ml carton of juice for $3.00,ben buys eight donuts and one 300ml carton of juice for $6.50 How much is one donut? How much is one carton of drink?

Answers

Complete Question

Max buys six donuts and a 300ml carton of juice for $3.50,susie buys four donuts and two 300ml carton of juice for $3.00,ben buys eight donuts and five 300ml carton of juice for $6.50 How much is one donut? How much is one carton of drink

Answer:

The cost of

1 donut = x = $0.50

300ml carton of juice = y = $0.50

Step-by-step explanation:

Let the cost of

1 donut = x

300ml carton of juice = y

Max buys six donuts and a 300ml carton of juice for $3.50

6x + y = 3.50.....Equation 1

y = 3.50 - 6x

Susie buys four donuts and two 300ml carton of juice for $3.00

4x + 2y = 3...... Equation 2

Ben buys eight donuts and one 300ml carton of juice for $6.50

8x + 5y = 6.50......Equation 3

We substitute 3.50 - 6x for y in Equation 2

4x + 2y = 3...... Equation 2

4x + 2(3.50 - 6x) = 3

4x + 7 - 12x = 3

Collect like terms

4x - 12x = 3 - 7

-8x = -4

x = -4/-8

x = $0.50

Solving for y

y = 3.50 - 6x

y = 3.50 - 6(0.50)

y = 3.50 - 3.00

y = $0.50

Therefore:

The cost of

1 donut = x = $0.50

300ml carton of juice = y = $0.50

If the length of a basketball court is 32 meters and the width is 9 meters, what is the diagonal of the basketball court? Round to the nearest tenth, if needed.

A. 33.2

B. 23

C. 30.7

D. 41

Answers

do 32 times 9 and i think you get the right answer

Answer:

the answer is a

Step-by-step explanation:

Olive has 600 fruit trees. Some of the trees are apple trees. The rest of the trees are pears trees and plum trees in the ratio of 7:5 there are 175 plum trees what is the fraction of apple trees

Answers

Answer: 3/10

Step-by-step explanation:

Since the rest of the trees are pears trees and plum trees in the ratio of 7:5 and there are 175 plum trees, the number of pear trees will be:

= 175 ÷ 5/7

= 175 × 7/5

= 245

Plum trees = 175

Pear trees = 245

Apple trees = 600 - (175 + 245)

= 600 - 420

= 180

Fraction of apple trees = Number of apple trees / Total number of trees

= 180/600

= 3/10

En el puenlo de tamalemeque desean construir un parque de forma rectangular con un camino diagonal cuanto debe medir el camino si el parque deberia tener de 80 metros de largo y 60 de ancho como se puede determinar la medida,argumente su respuesta utilizando lo que sabe de matematicas

Answers

Answer:

El camino diagonal debe medir 100 metros de largo.

       

Step-by-step explanation:

Podemos encontrar el camino usando Pitágoras:

[tex] D^{2} = L^{2} + A^{2} [/tex]

En donde:        

D: es el camino diagonal = hipotenusa

L: es el largo = 80 m = cateto

A: es el ancho = 60 m = cateto

Entonces, el camino diagonal es:

[tex] D = \sqrt{L^{2} + A^{2}} = \sqrt{(80 m)^{2} + (60 m)^{2}} = 100 m [/tex]

Por lo tanto, el camino diagonal debe medir 100 metros de largo.

Espero que te sea de utilidad!

Hayden reaches into his dresser and pulls out a red shirt, but does not like it and throws in onto the bed. What is the chance that the next shirt he pulls out of the dresser will be Purple?
A. 2/10
B. 4 in 10 chance
C. 4 in 9 chance
D. 1/9 chance

Answers

Answer:

how many of each color are in the dresser?

Step-by-step explanation:

So assuming there are 10 shirts total, (since it wasn’t specified) and one red is taken out, there would be 9 shirts left. And out of that, the information needed is the indication of how many purple shirts there is, so if there’s one purple shirt, it’s D, if there’s 4, it’s C. Does that make sense?

What is Turtle divided by Kitten? YALL I NEED HELP ASAP ON THIS!!!!!!1

Answers

Answer:

rabbit!

Step-by-step explanation:

:-)

A_____is a ratio that compares two measures

Answers

Answer:

rate

Step-by-step explanation:

A rate is a ratio that compares two different quantities that have different units of measure.

The art club is designing a rectangular mural for the school hallway. Three
corners are located at (-1,-1),(-1, 1), and (4.1) on a coordinate plane. Find the
fourth vertex and graph the rectangle on the coordinate plane below.
Fourth vertex:

Answers

Answer:

The coordinates are (50, 103)

Step-by-step explanation:

The three hallways are AB, BC, CD.

The co-ordinate of D is (50, 75).

The school's flagpole is 28 meters right of the point D.

Hence the y-coordinate for the flagpole will be same as D, that is 75.

The x-coordinate will be (28 + 75) = 103.

The location of the school's flagpole will be represented by (50, 103)

The 4th vertex of the rectangle is given by D ( 4 , -1 ) and the graph is plotted

What is the Area of a Rectangle?

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the area of the rectangle be represented as S

Let the rectangle be represented as ABCD

The coordinates of A = A ( -1 , -1 )

The coordinates of B + B ( -1 , 1 )

The coordinates of C = C ( 4 , 1 )

So , the length of the rectangle = 4 units

The width of the rectangle = 2 units

So , the area of the rectangle S = 4 x 2 = 8 units

And , the 4th vertex of rectangle D = D ( 4 , -1 )

Hence , the coordinate D of rectangle is D ( 4 , -1 )

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A fruit sekker buts 50 boxes of mangoes each containing 100 m mangoes at the rate of ₹1200 per box he sells each mangoes for ₹20 find his total profit and profit %

Answers

Answer:

₹40000, 66.6%

Step-by-step explanation:

Given data

Number of boxes= 50

Cost per box= ₹1200

Total cost= 50*1200= ₹60000

Total number of mangoes in all 50 boxes= 50*100= 5000 mangoes

Cost price per mago= 60000/5000=  ₹12

Selling price per mango=  ₹20

profit = selling price- cost price

profit=  20-12

proft=  ₹8

Total profit = 8*5000

Total profit= ₹40000

%profit = 40000/60000*100

%profit= 0.666*100

%profit= 66.6%

i am finding the volume of a shape, the area is 20mm and the length is 5cm what is the answer?​

Answers

Answer:

Whereas the basic formula for the area of a rectangular shape is length × width, the basic formula for volume is length × width × height.So the volume of the cube having side 15 mm is 3375 cubic inches.

Different Ways to Find Volume

Solve for Volume by Space. All physical objects occupy space, and you can find the volume for some of them by measuring their physical dimensions. ...

Solve for Volume by Density and Mass. Density is defined as an object's mass per a given unit of volume. ...

Solve for Volume by Displacement.

Step-by-step explanation:

An arc is 70.7 meters long and is intercepted by a central angle 5pi/4 radians. Find the diameter of the circle

Answers

Answer:

36.008 or 36

Step-by-step explanation:

Use the equation for the length of any circular arc  

s = r(radians)  

s - length of a circular arc

r - radius  

radians - radian measure of the central angle  

Then, set-up the equation:  

s = r(radians)

70.7m = r(5pi/4)  

Get variable "r" on one side by multiplying both sides by 4/5pi, which should result in the following:  

r = 70.7m x 4/5pi  

then solve for r  

r = 282.8/5pi = 18.004  

The radius is half the diameter therefore just multiply the radius by 2  

d = 18.004 x 2  

= 36.008 or 36  

The diameter of the circle is 36 meters.

What is an arc?

The arc is a portion of the circumference of a circle.

We have been given that an arc is 70.7 meters long and is intercepted by a central angle of 5π/4 radians.

We have to determine the diameter of the circle

For the length of the circular arc, use the equation.

⇒ 70.7 m = R(5π/4)  

Multiply both sides by 4/5π to get the variable "R" on one side, which should get the following:

⇒ R  = 70.7 m × 4/5π

⇒ R = 282.8/5π

∵ π = 3.14

⇒ R = 282.8/5(3.14)

⇒ R = 18.004  

Since the radius is equivalent to half the diameter, simply double the radius by 2.  

⇒ D = 18.004 × 2  

⇒ D = 36.008 ≈ 36  

Hence, the diameter of the circle is 36 meters.

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A(n)______ contains variables,numbers, and at least one operation.

Answers

Answer:

algebraic expression. An expression that contains at least one variable, at least one numbers and at least one operation.

Step-by-step explanation:

Answer:

expressions

Step-by-step explanation:

this is how a definition in a textbook would be written. they just put a blank in

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